Kernel PCA and de-noising in feature spaces
Proceedings of the 1998 conference on Advances in neural information processing systems II
Level set methods: an overview and some recent results
Journal of Computational Physics
Shape Priors for Level Set Representations
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
Nonlinear Shape Statistics in Mumford-Shah Based Segmentation
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
Segmentation of Bone in Clinical Knee MRI Using Texture-Based Geodesic Active Contours
MICCAI '98 Proceedings of the First International Conference on Medical Image Computing and Computer-Assisted Intervention
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Gradient flows and geometric active contour models
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Geometric Level Set Methods in Imaging,Vision,and Graphics
Geometric Level Set Methods in Imaging,Vision,and Graphics
Approximations of Shape Metrics and Application to Shape Warping and Empirical Shape Statistics
Foundations of Computational Mathematics
Intrinsic dimensionality estimation of submanifolds in Rd
ICML '05 Proceedings of the 22nd international conference on Machine learning
Shape-Based Approach to Robust Image Segmentation using Kernel PCA
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
IEEE Transactions on Pattern Analysis and Machine Intelligence
Intrinsic Statistics on Riemannian Manifolds: Basic Tools for Geometric Measurements
Journal of Mathematical Imaging and Vision
Geodesic Curves for Analysis of Continuous Implicit Shapes
ICPR '06 Proceedings of the 18th International Conference on Pattern Recognition - Volume 01
Data Fusion and Multicue Data Matching by Diffusion Maps
IEEE Transactions on Pattern Analysis and Machine Intelligence
Pre-image as Karcher Mean Using Diffusion Maps: Application to Shape and Image Denoising
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
From graphs to manifolds – weak and strong pointwise consistency of graph laplacians
COLT'05 Proceedings of the 18th annual conference on Learning Theory
Global structure constrained local shape prior estimation for medical image segmentation
Computer Vision and Image Understanding
| Hi-index | 0.00 |
Statistical analysis has proven very successful in the image processing community. Linear methods such as principal component analysis (PCA) measure the degree of correlation in datasets to extract meaningful information from high-dimensional data. PCA was successfully applied in several applications such as image segmentation with shape priors and image denoising. The major assumption in these applications is that the dataspace is a linear space. However, this assumption is mainly wrong and as a consequence several non-linear methods were developed, among which diffusion maps were recently proposed. In this paper we develop a variational framework to compute the pre-image using diffusion maps. The key-problem of pre-image determination consists of, given its embedding, recovering a point. Therefore we propose to model the underlying manifold as the set of Karcher means of close sample points. This non-linear interpolation is particularly well-adapted to the case of shapes and images. We then define the pre-image as an interpolation with the targeted embedding. The new methodology can then be used for regularization in image segmentation as well as for shape and image denoising. We demonstrate our method by testing our new non-linear shape prior for shape segmentation of partially occluded objects. Further, we report results on denoising 2D images and 3D shapes and demonstrate the superiority of our pre-image method compared to several state-of-the-art techniques in shape and image denoising based on statistical learning techniques.